title: Bayesian statistical inference enhances the interpretation of contemporary randomized controlled trials.
abstract: OBJECTIVE
  Randomized trials generally use "frequentist" statistics based on P-values and 95% confidence intervals. Frequentist methods have limitations that might be overcome, in part, by Bayesian inference. To illustrate these advantages, we re-analyzed randomized trials published in four general medical journals during 2004.
  
  
  METHODS
  We used Medline to identify randomized superiority trials with two parallel arms, individual-level randomization and dichotomous or time-to-event primary outcomes. Studies with P<0.05 in favor of the intervention were deemed "positive"; otherwise, they were "negative." We used several prior distributions and exact conjugate analyses to calculate Bayesian posterior probabilities for clinically relevant effects.
  
  
  RESULTS
  Of 88 included studies, 39 were positive using a frequentist analysis. Although the Bayesian posterior probabilities of any benefit (relative risk or hazard ratio<1) were high in positive studies, these probabilities were lower and variable for larger benefits. The positive studies had only moderate probabilities for exceeding the effects that were assumed for calculating the sample size. By comparison, there were moderate probabilities of any benefit in negative studies.
  
  
  CONCLUSIONS
  Bayesian and frequentist analyses complement each other when interpreting the results of randomized trials. Future reports of randomized trials should include both.
authors.affiliation: Department of Health Policy Management and Evaluation, University of Toronto, Toronto, Ontario, Canada. d.wijeysundera@utoronto.ca
authors.forename: Duminda N
authors.initials: DN
authors.lastname: Wijeysundera
authors.forename: Peter C
authors.initials: PC
authors.lastname: Austin
authors.forename: Janet E
authors.initials: JE
authors.lastname: Hux
authors.forename: W Scott
authors.initials: WS
authors.lastname: Beattie
authors.forename: Andreas
authors.initials: A
authors.lastname: Laupacis
mesh_terms: D001499:Bayes Theorem; D001699:Biometry / Q000379:methods*; D003627:Data Interpretation, Statistical; D019317:Evidence-Based Medicine / Q000706:statistics & numerical data; D015233:Models, Statistical; D011336:Probability; D016032:Randomized Controlled Trials as Topic / Q000706:statistics & numerical data*; D012107:Research Design